In this paper, the efficient multi-step differential transform method (EMsDTM) is applied to get the accurate approximate solutions for strongly nonlinear duffing oscillator. The main improvement of EMsDTM which is to reduce the number of arithmetic operations, is thoroughly investigated and compared with the classic multi-step differential transform method (MsDTM). To illustrate the applicabil...

In this paper, the effect of elastic foundation on the out of plane displacement of functionally graded circular plates using differential transform method is presented. Differential transform method is a semi-analytical-numerical solution technique that is capable to solve various types of differential equations. Using this method, governing differential equations are transformed into recursiv...

in this article, vibration analysis of an euler-bernoulli beam resting on a pasternak-type foundation is studied. the governing equation is solved by using a spectral finite element model (sfem). the solution involves calculating wave and time responses of the beam. the fast fourier transform function is used for temporal discretization of the governing partial differential equation into a set ...

in this article we have considered a non-standard finite difference method for the solution of second order  fredholm integro differential equation type initial value problems. the non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the fredholm integro-differential equation into a system of equations. we have also developed a numerical met...

in this paper, the differential transform method and padé approximation (dtm-padé) is applied to obtain the approximate analytical solutions of the mhd flow and heat transfer of a nanofluid over a nonlinearly stretching permeable sheet in porous. the similarity solution is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations...

In this paper, the differential transform method and Padé approximation (DTM-Padé) is applied to obtain the approximate analytical solutions of the MHD flow and heat transfer of a nanofluid over a nonlinearly stretching permeable sheet in porous. The similarity solution is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations...

Four-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of four-dimensional differential transform, exact solutions of nonlinear system of partial differential equations have been investigated. The results of the present method are compared very well with analytical solution of the system. Diff...

In this paper, buckling and free vibration analysis of a circular tapered nanoplate subjected to in-plane forces were studied. The linear variation of the plate thickness was considered in radial direction. Nonlocal elasticity theory was employed to capture size-dependent effects. The Raleigh-Ritz method and differential transform method were utilized to obtain the frequency equations for simpl...